Let G=(V,E,F) be an embedding of a graph and a,b,c belong to {0,1}. A labeling type (a,b,c) is assignment labels from the set {1,2,...,a|V|+b|E|+c|F|} so that each vertex receives labels, edge b face c no label used more than once. If weight every s-sided face, defined as sum with vertices edges border equal some fixed constant w(s), then said face-magic. We investigate face-magic labelings all...

A magic labelling of a graph G with sum s is the edges by nonnegative integers such that for each vertex v∈V, labels all incident to v equal same number s. Stanley gave remarkable results on labellings, but distinct case much more complicated. We consider complete construction labellings given G. The idea illustrated in detail dealing three regular graphs and non-regular graph. give combinatori...

Assume that we have m identical graphs where the graphs consists of paths with k vertices where k is a positive integer. In this paper, we discuss certain labelling of the m graphs called c-Erdösian for some positive integers c. We regard labellings of the vertices of the graphs by positive integers, which induce the edge labels for the paths as the sum of the two incident vertex labels. They h...

let $p$ be a complex polynomial of the form $p(z)=zdisplaystyleprod_{k=1}^{n-1}(z-z_{k})$,where $|z_k|ge 1,1le kle n-1$ then $ p^prime(z)ne 0$. if $|z|

An edge magic total labeling of a graph with p vertices and q edges is a bijection from the set of vertices and edges to 1, 2, . . . , p+ q such that for every edge the sums of the label of the edge and the label of its two end vertices are constant. Otherwise if the sum is distinct, it is said to be an edge-antimagic total labeling. A graph is called edgeantimagic if it admits edge-antimagic t...

In this paper, we are studying vertex-magic total labelings of simple graphs. We introduce a procedure called mutation which transforms one labeling into another by swapping sets of edges among vertices. The result of a mutation may be a different labeling of the same graph or a labeling of a different graph. Mutation proves to be a remarkably fruitful process— for example we are able to genera...

General methods for the construction of magic squares of any order have been searched for centuries. Several " standard strategies " have been found for this purpose, such as the " knight movement " , or the construction of bordered magic squares, which played an important role in the development of general methods. What we try to do here is to give a general and comprehensive approach to the c...

Graph labellings have been a very fruitful area of research in the last four decades. However, despite the staggering number of papers published in the field (over 1000), few general results are available, and most papers deal with particular classes of graphs and methods. Here we approach the problem from the computational viewpoint, and in a quite general way. We present the existence problem...

Model-generation based theorem provers such as SATCHMO and MGTP suffer from a combinatorial explosion of the search space caused by clauses irrelevant to the goal (negative clause) to be solved. To avoid this, two typical methods have been proposed. One is relevancy testing implemented in SATCHMORE by Loveland et al., and the other is non-Horn magic sets that are the extension of Horn magic set...